Radian to Degree: Radian and degree are the two basic geometrical units of angular measurement. They are two different measuring units, co-related with each other. They are convertible units. We can convert radians to degrees and also degrees to radians very easily. Before diving into the treasured knowledge of radians to degree conversion, let us revise the concept of radians and degrees.

Radian is the SI unit used to measure an angle. It plays a major role in trigonometry and is also useful in physics, mathematics, prefixes, etc. On the other side, a Degree is considered a non-SI unit. It is commonly used to divide a circle into smaller parts for easier measurement and reference. For example, right angles are 90 degrees, and a straight line corresponds to 180 degrees.

Explore more: Radian And Degree Measure

Formulas to convert radians to degrees

How to Convert Radians to Degrees?

Are you searching for how to convert radians to degrees? You are at the right site. In this article, we will relate radians with degrees in simple 4 conversion steps with solved examples.

A complete revolution of a circle is indicated by 2π (in terms of radians) or 360° (in terms of degrees).

Therefore. Radian and degree may be expressed as;

2π radian = 360 degrees

By dividing both sides by 2 we get;

π radian = 180 degrees

The formula for radians to degrees conversion is mentioned below.

\text{   degree} = \frac{180}{\pi}\text{x Angle in radian}

Where:

“radians” is the value in radians that you want to convert.

“pi” is the mathematical constant approximately equal to 3.14159.

Following are the steps to convert radians to degrees.

Step 1.  Write the angle’s numerical value given in radians in the equation.

Step 2. Multiply the value of the radian written in the equation by 180/π

Step 3. Cancel the common numerical factors to simplify the equation.

Step 4 The simplified result represents the angle measurement in radian

Also Refer: What are Supplementary units? How many radians account for the circumference of circle?

How to convert radians to degrees

Solved Examples

Q1 Convert 10π/9 radians to degrees

1st Method

Solution; Using the formula

\text{  degree} = \frac{180}{\pi}\text{x Angle in radian}

put the value of the angle in radians

\text{   degree} = (\frac{180}{\pi})(\frac{ 10\pi}{9})
\text{  degree} = {20}\text{  x 200}
\text{  degree} = {200°}

2nd Method:

Radian to degree conversion can also be determined by the alternative method

180^o=\pi \text{ radians} 
\text{  1 radian} = \frac{180}{\pi}
\text{ 1 radian} = 57.3^o

To determine 10π/9 radians in degrees, Multiply both sides by 10π divide by 9

  {1\left(\frac{10\pi}{9}\right)=57.3^o\left(\frac{10\pi}{9}\right)}
  {\left(\frac{10\pi}{9}\right)radians=57.3^o(3.49)}
  {\left(\frac{10\pi}{9}\right)radians=200^o}

From the above calculations, it is clear that 10π/9 radians is equal to 200 degrees

Q2 What is π/6 radians in degrees

There are two methods for the conversion of π/6 radians to degrees.

1st Method

Solution: Using the conversion formula

\text{  degree} = \frac{180}{\pi}\text{x Angle in radian}

To determine π/6 radians in degrees. Put it in the above equation

\text{  degree} = (\frac{180}{\pi})(\frac{ \pi}{6})
\text{  degree} = (\frac{180}{6})
\text{  degree} = {30°}

2nd Method

In this alternative conversion method, we use radians to degrees relation

\text{ 1 radian} = 57.3^o

multiply π/6 on both sides

  {1\left(\frac{\pi}{6}\right)=57.3^o\left(\frac{\pi}{6}\right)}
  {\left(\frac{\pi}{6}\right)radians=57.3^o(0.524)}
  {\left(\frac{\pi}{6}\right)radians=30^o}

It is clear that π/6 radians in degrees is equal to 30 degrees

Q3 Convert 11π/6 radians to degrees

1st Method

Use the conversion formula

\text{  degree} = \frac{180}{\pi}\text{x Angle in radian}

put Angle in radian= 11π/6 rad

\text{  degree} = (\frac{180}{\pi})(\frac{11 \pi}{6})
\text{  degree} = {(30)(11)}
\text{  degree} = {330°}

2nd Method

Using the relation

\text{ 1 radian} = 57.3^o

To find the 11π/6 radians in degrees. multiply it on both sides

  {1\left(\frac{11\pi}{6}\right)=57.3^o\left(\frac{11\pi}{6}\right)}
  {\left(\frac{11\pi}{6}\right)radians=57.3^o(5.757)}
  {\left(\frac{11\pi}{6}\right)radians=330^o}

It can be concluded 11π/6 radians to degrees is equal to 330 degrees

Q4 What π/12 radians correspond to degrees?

The two possible methods to convert π/12 radians to degrees are given below.

1st Method

Using formula

\text{  degree} = \frac{180}{\pi}\text{x Angle in radian}

putting the value of radian

\text{  degree} = (\frac{180}{\pi})(\frac{\pi}{12})
\text{  degree} = (\frac{180}{12})
\text{  degree} = (\frac{180}{12})
\text{  degree} = {15°}

2nd Method

Using the radian to degree mathematical relation

\text{ 1 radian} = 57.3^o

Multiply π/12 on both sides

  {1\left(\frac{\pi}{12}\right)=57.3^o\left(\frac{\pi}{12}\right)}
  {\left(\frac{\pi}{12}\right)radians=57.3^o(0.262)}
  {\left(\frac{\pi}{12}\right)radians=15^o}

It is concluded that π/12 radians in degrees are equal to 15 degrees.

Q5 Convert 7.854 radians to Degrees

1st Method

Using the conversion formula

\text{  degree} = \frac{180}{\pi}\text{x Angle in radian}

Putting the value of radian

\text{  degree} = \frac{180}{\pi}\text{x 7.854}
\text{  degree} = {(57.325)(7.584)}
\text{  degree} = {450°}

2nd Method

By using the mathematical relations between radian and degree

\text{ 1 radian} = 57.3^o

Multiply 7.584 on both sides

\text{  1 (57.3) radian} = {(57.3)(7.584)}
\text{  57.3 radian} = {450^o}

It is clear that there are 450 degrees in 7.584 radians

Radian To Degree Conversion Table

In the given table there are some common angles in radians that are converted to degrees. Go through the table to make your concept clearer about radian to degree conversion.

Also Check Out: Detailed Note on radian with common and important questions related to it

Table of radian to degree conversion

Some Common Angle Conversions

Here is the infographic of some common angle conversions. Go through it.

common radians to degrees conversion infographic

Frequently Asked Questions – FAQs

Q1 How to convert radians to degrees?

For radians to degrees conversion, we have a simple conversion formula

\text{   degree} = \frac{180}{\pi}\text{x Angle in radian}

Just multiply the numerical value of the angle in radians by 180 divided by pi, and you will get the corresponding radians in degrees.

Q2 What is the formula for radian to degree conversion?

There is a very simple conversion formula between the radian and degree.

\text{   degree} =\text{ Angle in radian x } \frac{180}{\pi}

The above formula is used for radian conversion to degrees. By arranging we can also determine the degree conversion to radians.

Q3 What is the value of 1 degree?

The value of 1 degree in terms of radians is equivalent to 0.0174 rad.

Check Out Other Conversion Related Topics

Conversion Between Radian and Degree MeasuresHow Do you convert 180 degrees to radians
Formulas for the conversion between radian and degreeWhat is 45 degrees in Radians
Convert 90 degrees to radiansHow to determine the conversion relation between radian and degree?

Also Check Out

What is radian and steradian give their mathematical relation with examples.How many radians account for the circumference of the circle?
What are supplementary units? Write their dimensions How many steradians account for the circumference of the sphere?
What do you know about radian as SI unit?Radian and Degree Measure

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